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Properties

Label 1900.4.i
Level $1900$
Weight $4$
Character orbit 1900.i
Rep. character $\chi_{1900}(201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $190$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1900, [\chi])\).

Total New Old
Modular forms 1836 190 1646
Cusp forms 1764 190 1574
Eisenstein series 72 0 72

Trace form

\( 190 q + 7 q^{3} - 12 q^{7} - 860 q^{9} + O(q^{10}) \) \( 190 q + 7 q^{3} - 12 q^{7} - 860 q^{9} - 50 q^{11} + 40 q^{13} - 80 q^{17} + 193 q^{19} - 66 q^{21} - 36 q^{23} - 482 q^{27} - 12 q^{29} + 336 q^{31} + 479 q^{33} - 208 q^{37} - 396 q^{39} - 53 q^{41} - 44 q^{43} + 426 q^{47} + 10662 q^{49} - 1208 q^{51} - 76 q^{53} - 1006 q^{57} + 163 q^{59} - 296 q^{61} + 944 q^{63} + 627 q^{67} - 2724 q^{69} - 274 q^{71} - 803 q^{73} + 3244 q^{77} - 1292 q^{79} - 8003 q^{81} + 1622 q^{83} - 3268 q^{87} - 1160 q^{89} + 592 q^{91} - 808 q^{93} + 931 q^{97} + 3060 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)